# Yifeng Xu

less info
reputation
111
bio website location age member for 1 year, 2 months seen 23 hours ago profile views 378

# 101 Questions

 20 Does there exist a sequence $\{a_n\}_{n\ge1}$ with $a_n < a_{n+1}+a_{n^2}$ such that $\sum_{n=1}^{\infty}a_n$ converges? 13 Showing that $|\cos x|+|\cos 2x|+\cdots+|\cos 2^nx|\geq \dfrac{n}{2\sqrt{2}}$ 9 Let $a_k=\frac1{\binom{n}k}$, $b_k=2^{k-n}$. Compute $\sum_{k=1}^n\frac{a_k-b_k}k$ 9 Find the maximum and minimum of $\sum_{i=1}^{n-1}x_ix_{i+1}$ subject to $\sum_{i=1}^nx_i^2=1$. 9 Prove that $\int_0^1|f''(x)|dx\ge4.$

# 1,738 Reputation

 +10 Minimizing the distance between points in two sets +5 2 is a primitive root mod $3^h$ for any positive integer $h$ -2 Evaluate $\lim_{n\to\infty}n\int_0^1x^nf(x)dx$ +5 Prove that there exists $t$ such that $0\le t\le T$ and $\int_0^Te^{-x}y'y''dx=\int_0^ty'y''dx$.

 2 Finding the index such that all partial sums are nonnegative 0 Find the maximum and minimum of $\sum_{i=1}^{n-1}x_ix_{i+1}$ subject to $\sum_{i=1}^nx_i^2=1$. 0 $\sum_{i=1}^nx_i^2+2\sum_{1\le k 3j$, there exists positive integers $s,t$ such that $k > |\sqrt{s}-\sqrt{t}| > j$

# 87 Tags

 2 contest-math × 59 0 integration × 19 2 algorithms × 4 0 measure-theory × 16 2 integer-programming × 2 0 sequences-and-series × 13 0 analysis × 59 0 elementary-number-theory × 11 0 calculus × 20 0 limit × 10

# 4 Accounts

 Mathematics 1,738 rep 111 Stack Overflow 115 rep 5 Theoretical Computer Science 101 rep Programming Puzzles & Code Golf 101 rep